Quadrature solution of ordinary and partial differential equations

Matlab : Numerical Solution of Ordinary Differential Equations

Matlab has facilities for the numerical solution of ordinary differential equations (ODEs) of any order. In this document we first consider the solution of a first order ODE. Higher order ODEs can be solved using the same methods, with the higher order equations first having to be reformulated as a system of first order equations. Techniques for solving the first order and second order equation...

On parallel solution of ordinary differential equations

In this paper the performance of a parallel iterated Runge-Kutta method is compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince methods. It was found that, typically, the runtime for the parallel method is comparable to that of the serial versions, thought it uses considerably more computational resources. A new algorithm is proposed where full parallelization is used ...

Numerical solution of ordinary differential equations

Ordinary differential equations are ubiquitous in science and engineering: in geometry and mechanics from the first examples onwards (Newton, Leibniz, Euler, Lagrange), in chemical reaction kinetics, molecular dynamics, electronic circuits, population dynamics, and many more application areas. They also arise, after semidiscretization in space, in the numerical treatment of time-dependent parti...

Numerical Solution of Ordinary Differential Equations

Solution of Partial Differential Equations

We encounter partial differential equations routinely in transport phenomena. Some examples are unsteady flow in a channel, steady heat transfer to a fluid flowing through a pipe, and mass transport to a falling liquid film. Here, we shall learn a method for solving partial differential equations that complements the technique of separation of variables. We shall also learn when the method can ...